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Simplifying -5x2 + 72x + 378 = 1990 Reorder the terms: 378 + 72x + -5x2 = 1990 Solving 378 + 72x + -5x2 = 1990 Solving for variable 'x'. Reorder the terms: 378 + -1990 + 72x + -5x2 = 1990 + -1990 Combine like terms: 378 + -1990 = -1612 -1612 + 72x + -5x2 = 1990 + -1990 Combine like terms: 1990 + -1990 = 0 -1612 + 72x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 322.4 + -14.4x + x2 = 0 Move the constant term to the right: Add '-322.4' to each side of the equation. 322.4 + -14.4x + -322.4 + x2 = 0 + -322.4 Reorder the terms: 322.4 + -322.4 + -14.4x + x2 = 0 + -322.4 Combine like terms: 322.4 + -322.4 = 0.0 0.0 + -14.4x + x2 = 0 + -322.4 -14.4x + x2 = 0 + -322.4 Combine like terms: 0 + -322.4 = -322.4 -14.4x + x2 = -322.4 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = -322.4 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = -322.4 + 51.84 Combine like terms: -322.4 + 51.84 = -270.56 51.84 + -14.4x + x2 = -270.56 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = -270.56 Can't calculate square root of the right side. The solution to this equation could not be determined.
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